The Rolf Nevanlinna Prize is awarded by the International Mathematical Union for “outstanding contributions in mathematical aspects of information sciences”. Jon Kleinberg, the 2006 recipient of the Nevanlinna Prize, was cited by the prize committee for his “deep, creative, and insightful contributions to the mathematical theory of the global information environment”. Our purpose is to present ...

This is the Part II of our paper “Height functions for motives”. We consider more general period domains and height on sets motives. also corresponding Hodge theoretic variant Nevanlinna theory.

A. Orders of Growth on Algebraic Varieties . . . . . . . . . . . 4 w 1. Review of the Classical Theory . . . . . . . . . . . . . 4 w 2. Generalization to Algebraic Varieties . . . . . . . . . . . 6 w 3. Exhaustion Functions and K~ihler Metrics on Special Affine Varieties . . . . . . . . . . . . . . . . . . . . . . . 9 84. Order of Growth of Analytic Sets . . . . . . . . . . . . 13 w 5. Order of...

We propose a new approach to the value distribution theory of entire holomorphic curves. We define a packing density of an entire holomorphic curve, and show that it has various non-trivial properties. We prove a gap theorem for holomorphic maps from elliptic curves to the complex projective space, and study the relation between theta functions and our packing problem. Applying the Nevanlinna t...

6 The multiplier space and other spaces intrinsic to D theory 24 6.1 Multipliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 6.2 The weakly factored space D D and its dual . . . . . . . . . . . 25 6.3 The Corona Theorem . . . . . . . . . . . . . . . . . . . . . . . . 27 6.3.1 The ∂-equation in the Dirichlet Space . . . . . . . . . . . 28 6.3.2 Corona Theorems and Complete Nev...